A State of Football, Part II: Inter-Player Dynamics
In my previous post I outlined some of the basics behind considering football as a dynamical system and how we might proceed to synthesize an attractor to study the movement dynamics of a team. To summarize, a team can be described by a set of variables like its center of mass (i.e. position) and theContinue reading “A State of Football, Part II: Inter-Player Dynamics”
A State of Football, Part I: Attractors & Space Occupation
The first entry in a two-part series going over the intersection of topological data analysis with dynamical systems theory – in this case, how we can understand team space occupation by constructing attractors for a football match.
Geometric Methods in High Energy Physics
Problems are only as hard as their representations and this particular one about simulating trajectories in particle decay seems quite complex until it’s framed as a geometric question.
Mathematical Design in the Islamic World
Geometric patterns are a prevalent feature in Islamic art and architecture, the complexity of which ranges from simple polygon tiling to multi-layered, fractal structures. Here I look at some famous patterns which occur in Islamic geometric design, and try to break down some of the neat mathematical features behind each one. In addition, I’ve added in a few interactive modules to play around with, which hopefully are a) fun and b) provide a better visual intuition.
Geometric Methods in Time Series Analysis
Math, like football, is less about technical brilliance and more about applying the right idea at the right time with a bit of creativity. Here I demonstrate how a real problem prevalent in time series analysis has a simple and robust solution using elementary geometry and algebra; meanwhile, the typical approach invoking calculus or machine learning could quickly lead to complications.
The Messi Project, Part II: LM10 vs CR7
Perhaps the greatest footballing rivalry ever, Lionel Messi and Cristiano Ronaldo have consistently topped the charts of football in terms of performance stats and accolades; and yet they couldn’t be more different in terms of their footballing style. In this post I introduce topological data analysis and how it can tell us about what exactly makes these players so special.
The Messi Project, Part I: The Influence of LM10
Despite playing at FC Barcelona in the Spanish La Liga for over 10 years, Lionel Messi seems to continually outperform himself season after season. In this post, I look beyond goals and assist tallies and analyze the Barcelona passing network in order to measure Messi’s impact over the years.
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